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bonanova

Thank goodness, no remainder is chasing me

Question

Ten years ago I called attention to a number that when divided by a single integer p it left a remainder of p-1. (Help, a remainder is chasing me) Here is a chance to construct a nine-digit number, a permutation of { 1 2 3 4 5 6 7 8 9 } that has no remainders, sort of. The task is to permute { 1 2 3 4 5 6 7 8 9 } to create a number whose first n digits is a multiple of n for any single-digit n.

For example, consider 123654987. Its first 2 digits (12) are divisible by 2. It's first 5 digits (12365) are divisible by 5.

However this is not a solution, since 1236549 is not a multiple of 7.

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Spoiler

381654729

  • 3/1 = 3
  • 38/2 = 14
  • 381/3 = 127
  • 3816/4 = 954
  • 38165/5 = 7633
  • 381654/6 = 63609
  • 3816547/7 = 545221
  • 38165472/8 = 4770684
  • 381654729/9 = 42406081

 

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On 2/8/2018 at 10:40 AM, Pickett said:
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Close, check the second case.

Brain fart. Nice solution.

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